Cassava Sciences Inc (SAVA)

[investingdog]

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Answer
To calculate the statistical significance of the clinical trial results, we need to perform a hypothesis test comparing the mean ADA-cog scores between the drug and placebo groups. Given the information provided, we can conduct a two-sample t-test assuming equal variances.

Assumptions:
• The data follows a normal distribution.
• The standard deviation of 13 is the same for both groups.
Null Hypothesis (H0): There is no difference in mean ADA-cog scores between the drug and placebo groups.
Alternative Hypothesis (H1): There is a difference in mean ADA-cog scores between the drug and placebo groups.

Let's define the variables:
• n1 = sample size of the placebo group = 320 (assuming equal group sizes)
• n2 = sample size of the drug group = 320 (assuming equal group sizes)
• µ1 = mean ADA-cog score for the placebo group = 20
• µ2 = mean ADA-cog score for the drug group = 16
• s = standard deviation = 13 (assumed to be the same for both groups)
The test statistic for the two-sample t-test is calculated as:

t = (µ1 - µ2) / sqrt[(s^2/n1) + (s^2/n2)]
t = (20 - 16) / sqrt[(13^2/320) + (13^2/320)]
t = 4 / sqrt(0.5294)
t = 4 / 0.7275
t = 5.50

With 638 degrees of freedom (n1 + n2 - 2 = 320 + 320 - 2 = 638), the critical value for a two-tailed test at the 5% significance level is approximately 1.96.

Since the calculated t-value (5.50) is greater than the critical value (1.96), we reject the null hypothesis. This means that the difference in mean ADA-cog scores between the drug and placebo groups is statistically significant at the 5% level.

Therefore, based on the given information, the clinical trial results show a statistically significant difference in mean ADA-cog scores between the drug and placebo groups, with the drug group having a lower (better) mean score of 16 compared to 20 in the placebo group.

In summary, a t-statistic of 5.5 corresponds to an extremely small p-value, indicating that the null hypothesis can be rejected with a high degree of confidence. The exact p-value depends on the degrees of freedom, but is certainly less than 0.00001 for any reasonable sample size.